Diffuse Optical Tomography with an Inaccurately Known Domain Boundary

Abstract. Diffuse optical tomography (DOT) is an imaging modality in which images of the optical properties of a biological tissue, specifically diffusion [Formula: see text] and absorption [Formula: see text], are estimated based on measurements of near-infrared light on the surface of the body. In practical applications, one often lacks exact knowledge of the measurement domain boundary. This poses a significant challenge, as inaccuracies in the boundary shape of the computational domain may result in substantial artifacts in the reconstructed images. In this study, the following two results are achieved in a two-dimensional setting: (i) when the measurement domain [Formula: see text] is known, it is shown that knowledge of the Robin-to-Neumann map for two modulation frequencies uniquely determines [Formula: see text] and [Formula: see text], both assumed to be isotropic. (ii) When the measurement domain [Formula: see text] is not exactly known, a method is proposed for simultaneous reconstruction of [Formula: see text] and [Formula: see text] as well as the boundary [Formula: see text]. For this, DOT measurements are needed for two modulation frequencies. This approach yields reconstructed coefficients that are a conformal deformation of the true coefficients in the exact domain. The new method is demonstrated using simulated noisy data.